UNC ECON 3125 – Example 2 A market (or industry)
Example #2A market (or industry) demand curve is described byQ = 50 – 0.5 PThe monopolist firm’s cost function isTC = 10 + 4 Qa. Find the profit-maximizing quantity and price.b. If the industry is regulated in a way that requires it to set P = MC, how much profit will themonopolist make?>>>>>>>>>>a. MR = MC MR = MC 0.5P = 50 – Q 100 – 4Q = 4 P = 100 – 2Q 96 = 4Q TR = (100 – 2Q)Q Q = 24 TR = 100Q – 2Q2 Plug in to get MR = 100 – 4Q P = 100 – 2(24) MC = 4 P = 100 – 48 = Price = $52 MC = 4 Profit = TR – TC MC = Price = 4 Profit = (4 x 48) – (10 + 4(48)) Q = 50 – 0.5P Profit = 192 – 10 – 192 Q = 50 – 0.5(4) Profit = -10 b. Q = 50 – 2Q = 48 2. A market (or industry) demand curve is described byQ = 600 – 0.5 PThe monopolist firm’s cost function isTC = 8,550 + 20Qa. Find the profit-maximizing quantity and price.b. If the monopoly is dissolved and then the market becomes perfectly competitive, how muchmore quantity will be produced?
